Diagram of patchy colloid model.
Examples of associated clusters with paths of AB bonds. Black lines represent an AB bond. Here we show 4-mer cycles, but cycles of all sizes are accounted for. Orange area gives surface of overlap of the A and B patches.
Numerical results 1 for the blockage integral Ψ which accounts for the steric hindrance between patches A and B, the probability that two colloids are oriented such that double bonding can occur I d , and the ring integrals Γ(3) and Γ(4) which are proportional to the number of ring states for 3-mer and 4-mer rings, respectively.
The fractions of colloids bonded k times X k for case I at η = 0.1 and ɛ* = 8 (top) and η = 0.35 and ɛ* = 7.5 (bottom). Curves give theory predictions and symbols give simulation results.
Same as Fig. 4 except for case II.
Fractions bonded at both patches A and B in the various cluster types, Eq. (45) , at η = 0.1 and ɛ* = 8 for case I (top) and case II (bottom). Curves give theory predictions and symbols give simulation values for . Insets give cycle fractions and . Larger cycle sizes are non-zero but negligible and are not shown.
Compressibility factor for case I colloids at bond angles α AB = 20° (top) and α AB = 45° (bottom) at association energies ɛ* = 2 (short dashed line – theory, triangles – simulation), ɛ* = 4 (long dashed line – theory, circles – simulation), and ɛ* = 8 (solid line – theory, squares – simulation).
Same as Fig. 7 except for case II.
Compressibility factor versus α AB at η = 0.1 and ɛ* = 8 (top) and η = 0.35 and ɛ* = 7.5 (bottom).
Phase diagrams T* = 1/ɛ* versus ρ* = ρd 3 for case II colloids at various bond angles α AB .
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